1. Field of the Invention
The present invention relates to the determination of the far field signature of, for instance, a marine seismic source.
In siesmic experiments, the measurable response x(t) is regarded as being composed of the impulse response of the earth g(t), convolved with the far field signature of a seismic source s(t), plus some noise n(t). thus EQU x(t)=s(t)*g(t)+n(t), (1)
where the asterisk * denotes convolution.
The object of initial data processing of the measurements is to recover the earth impulse response g(t) from the measurable quantity x(t) with as high a degree of fidelity as possible. In order to do this there are three basic requirements which must be met:
(1) The signal to noise ratio EQU .vertline.s(t)*g(t).vertline./.vertline.n(t) PA1 must be large. PA1 (2) The frequency bandwidth of the generated far-field signature s(t) must be broad. PA1 (3) The shape of the far field signature s(t) must be known. PA1 (a) By separation in time. The units are fired sequentially such that each one generates all its significant seismic radiation before the next one is fired. PA1 (b) By separation in space. The distance between spatially-separated elements must be greater than about a wavelength (of the lowest frequency of interest) for interaction to be negligible between them when they are generating seismic energy simultaneously.
This means that both the amplitude and phase as a function of frequency must be known.
All these three requirements are met if the seismic source produces a high-energy, broad bandwidth signature of known shape. In attempting to meet the first two requirements at sea, with seismic source arrays, it is usually the case that the third requirement is not met.
Marine seismic sources currently in use are of two types; point sources and arrays. Point sources are those which have dimensions which are small compared with the wavelengths of seismic radiation which they generate. Arrays are sources which are not small compared with the wavelengths of seismic radiation which they generate.
Some marine point seismic sources, notably air guns, generate low seismic energy in a band of frequencies which is generally too narrow for normal requirements. However, arrays of such sources are built to overcome the limitations of the individual guns. These arrays employ a number of guns of different sizes. Each size of gun generates seismic energy predominantly in a different part of the seismic spectrum, although the spectra of the guns of different sizes do overlap somewhat. The array of guns is designed to produce enough energy over a broad enough range of frequencies to satisfy the first two requirements mentioned hereinbefore. In order to preserve the essential design aim that the seismic energy generated be in the desired bandwidth, the guns are combined in units which are spaced sufficiently far apart to be essentially independent of each other, each unit consisting of one or more guns fairly close together. The units are small compared with a wavelength and are therefore basically point sources, but the dimensions of the whole array are usually of the order of a wavelength or more within the seismic bandwidth, and the array is not a point source.
Within such dimensions the basic source units do not behave entirely independently. The pressure wave generated by each unit radiates in all directions and impinges on all the other units, thus modifying their behaviour. Consequently the far field seismic pressure wave produced by the array of source units is not exactly equal to the sum of the signature of the individual source units acting independently. The interaction effects between the source units are not well understood and, as yet, there is no theory to predict exactly what the distorting effect of the interactions between source units within a seismic source array will be.
In order to meet the third requirement mentioned hereinbefore, it is essential to determine the far field signature of the seismic source array. This measurement is fraught with difficulties, and it is these difficulties which it is desired to overcome.
The basic problems with the measurement of the far field signature of a marine seismic source array is that the water on the continental shelf is too shallow to permit the measurement to be made over the required bandwidth.
The minimum range r.sub.1 at which a hydrophone can be placed below the array to measure the far field signature is derived in the Appendix 1 to the description of preferred embodiments given hereinafter and is: EQU r.sub.1 =f D.sup.2 /c (2)
where D is the length of the array, f is the frequency and c is the velocity of sound in sea water. At ranges less than this there will be phase distortion at frequency f. Any constraints on the magnitude of r.sub.1 become converted to simultaneous constraints on the high frequency fidelity of the measurement.
There is a risk of contamination of the measurement by the arrival of the sea floor reflection. This will affect all frequencies, especially the low frequencies, if it arrives too early. There must be sufficient depth of water below the far field hydrophone to avoid contamination.
If, for example, it is desired to measure the far field signature of a marine seismic source array of length 20 m, preserving frequencies up to 100 Hz, the high frequency constraint demands that the hydrophone be at least 30 m below the array. If most of the significant energy over the bandwidth of interest is generated within the first 200 ms, at least 150 m of water is required below the hydrophone to record the source signature properly. If the depth of the source array is 10 m, a total depth of water of 190 m is required. Most of the continental shelf which it is desired to explore is much shallower than this. It is therefore impossible to measure accurately the far signature of a typical array such as this. It will be necessry to suffer severe phase distortion at high frequencies, or sacrifice the tail of the signature to contamination by sea bottom reflections, or both.
2. Description of the Prior Art
This problem is well understood and there are two approaches which have been used to overcome it. The first is simply to take the array into deep water and to measure the far field signature there. This signature is then used in subsequent processing of data which are obtained using the same source array in shallow water. The second approach is to design the array such that the far field signature is as short as possible, so that very little processing of the data for removal of the signature is required. It is also often a good assumption, with this second approach, that the signature is minimum-phase and therefore it can be removed from the data if a good estimate of the power spectrum of the source signature can be obtained from the data. In practice, these two approaches are used together. That is, the source signature is designed to be short and the far field signature is measured in deep water before the array is used for production seismic surveying on the continental shelf.
One problem with the first approach is that it is usually very difficult to keep all the conditions constant. There are always small variations in, for example, the depth of the source array. This varies with the speed of the ship through the water, which is not the same as the speed of the ship over the sea floor, due to variations in currents. There are also variations in sea state, performance of individual guns, synchronization of the firing instants, air pressure delivered by the ship's compressors, etc. Also, individual guns stop working properly sometimes and it is not always worthwhile to stop the whole survey simply to repair one gun. Therefore surveying continues with a different source signature. For these reasons, the deep-water far field measurement of the source array is likely to differ from the signature generated by the array in normal use.
Another problem with the first approach is that there is no single far field signature. The array is directional; that is, the shape of the signature varies with the direction. This is caused by the finite size of the array and is further described in Appendix 1. Therefore any single far field measurement can determine the signature in only one direction. A whole set of measurements would be needed to obtain the full required directional response and, as surveying conditions change, this response also changes.
A problem with the second approach is that it is normally impossible to generate a signature which is short enough without relying very heavily on destructive interference of the tail-end energy radiated from individual guns. In other words, signal energy is directed sideways to make the downward-travelling wave short. This is an inefficient use of available energy and is expensive in ship-board compressors, etc. Furthermore these signatures are never short enough, and processing of the recorded data to compress the signature is usually regarded as essential to obtain the best results.
This processing depends on a reliable estimate of the signature being obtainable from the data. This estimate is made using statistical techniques. There is no way to determine whether the correct signature has been obtained. This is because the statistical techniques aim to solve one equation i.e. equation (1) with three unknowns. The correctness of the solution is as good as the statistical assumptions and these cannot be tested.